1. Parameters and confidence intervals
Until now, the research question at hand has been a question of comparison.
2. Research questions
What if, instead, the research question is one of estimation?
For example, "under which diet plan will participants lose more weight on average" is a comparative question and we use a hypothesis test. "How much should participants expect to lose on average" is an estimation question for which we use confidence intervals.
Or another example is the comparative question: "which of two car manufacturers are drivers more likely to recommend to their friends?" Hypothesis testing is used to analyze that question. But: "what percent of users are likely to recommend Subaru to their friends" is an estimation problem and we use confidence intervals to answer that question.
One more, the comparative question: "are education level and average income linearly related" is addressed with a hypothesis test. The estimation question: "for each additional year of education, what is the predicted average income" uses a confidence interval. OK, you see the pattern.
3. Parameter
For each of the estimation problems, we need to understand what a parameter is. A parameter is a numerical value from the population. So in the first example, the parameter is the true average amount that all dieters will lose on a particular program. In the second example, the parameter is the proportion of individuals in the population who recommend Subaru cars. And the last parameter is the average income of all individuals in the population with a particular education level.
4. Confidence interval
A confidence interval is a range of numbers that hopefully captures the true parameter value of interest. For example, at the end of the course, we'll be able to make conclusions along the lines of "we are 95% confident that somewhere between 12% and 34% of the entire population recommends Subarus."
That is, the goal in creating a confidence interval is to calculate a range of plausible values for the parameter of interest.
5. Let's practice!
OK, now it's your turn to practice what you've learned.